The field of the invention relates to synchronization of signals and, in particular, to a method of jointly performing synchronization, channel estimation and noise estimation using a least squares estimation method, e.g., in a radiocommunication system.
The cellular telephone industry has made phenomenal strides in commercial operations in the United States as well as the rest of the world. Growth in major metropolitan areas has far exceeded expectations and is rapidly outstripping system capacity. If this trend continues, the effects of this industry""s growth will soon reach even the smallest markets. Innovative solutions are required to meet these increasing capacity needs as well as maintain high quality service and avoid rising prices.
In mobile communication, the transmitted signal is often subjected to a time smearing effect created by the time dispersive nature of the channel, i.e., the air interface between a base station and a mobile station. The channel effects are estimated in the receiver part of a communication system, and used by the detector to aid in attempting to correctly deduce the information symbols that were transmitted thereto.
In a digital cellular system, xe2x80x9csymbolsxe2x80x9d are sent out from a transmitter, e.g. a mobile phone. A symbol in this case, e.g., systems as defined by the Global System for Mobile Communications (GSM) or Enhanced Data Rates for Global Evolution (EDGE), can be seen as a complex-valued number, where the information resides in the phase angle. GSM has defined 1 bit symbols with possible phase angles of 0 and xcfx80 radians. EDGE has defined 3 bit symbols, with possible phase angles of 0, xcfx80/4, xcfx80/2, 3xcfx80/4, xcfx80, 5xcfx80/4, 3xcfx80/2 and 7xcfx80/4 radians, respectively.
When sending a symbol, a pulse-shaped waveform is transmitted in the air. The symbol rate in both GSM and EDGE systems is 270,833 symbols per second, therefore, new symbol xe2x80x9cpulsesxe2x80x9d will be created by the transmitter each 3.7 xcexcs. A transmitted symbol pulse is split into several rays during its travel though the air which phenomena is referred to as multi-path propagation. Different rays typically travel along different paths on their way between transmitter and receiver antennas. Examples of items that cause multi-path distortion are reflections because of hills, buildings, vehicles etc. On the receiving side (e.g. a base station), the symbols will be detected thru complex-valued measurements of the received rays.
As an extreme example, e.g., in hilly terrain, consider that a specific symbol is smeared over 30 xcexcs, i.e., about eight times the original symbol period. To reconstruct such symbols the receiver can make measurements, Y(i), which contain a weighted sum of 8 transmitted symbols, S(ixe2x88x92k):
Y(i)=xcexa3H(k)*S(ixe2x88x92k); k=0 to 7;
wherein H(k) are the channel taps (complex-valued). Such a radio channel is often briefly referred to as an xe2x80x9c8 tap channel.xe2x80x9d
In order to time tune (xe2x80x9csynchronizexe2x80x9d) a receiver to a burst of received symbols, the position of a known data pattern within the burst is determined. In GSM systems, this pattern is referred to as a training sequence and is defined to be in the middle of each burst or timeslot. Normal Bursts (NB) in both GSM and EDGE contain a training sequence of 26 symbols as illustrated in FIG. 1, which symbols are complex-valued.
A primary issue confronting systems designers dealing with synchronization issues is determining, for example with respect to GSM systems and terminals, which group of 26 measurements performed on a received data burst at the receiver corresponds xe2x80x9cbestxe2x80x9d to the 26 training sequence symbols. A conventional GSM synchronization system, which is described in U.S. Pat. No. 5,373,507 (the disclosure of which is incorporated here by reference), addressed this challenge as follows.
After receiving a burst of data, the receiver processes it in a number of different steps to acquire synchronization. In a first step, the center of energy of a first vector, having e.g., M correlation values between a synchronization sequence and M parts of a signal frame, which are partially overlapping and mutually displaced by one sampling interval, is calculated. For example, by taking five consecutive correlation values to form a first vector and then shifting attention to the next five consecutive sampling values, two vectors are obtained with partially the same elements which are time displaced by one sampling interval. FIG. 2 depicts a correlation-time diagram in which the sampling instances n run along the X-axis and the squared magnitudes of the correlations between the locally generated training sequence and the received signal run along the Y-axis. The center of energy w is calculated in accordance with the formula:   w  =                              ∑                      M            -            1                                    k          =          0                    ⁢              k        ⁢                              "LeftBracketingBar"                          c              ⁡                              (                k                )                                      "RightBracketingBar"                    2                                              ∑                      M            -            1                                    k          =          0                    ⁢                        "LeftBracketingBar"                      c            ⁡                          (              k              )                                "RightBracketingBar"                2            
where M is the number of correlation values e.g., 11. The obtained value is rounded to a preliminary window position m, by rounding the obtained value w to the nearest integer.
In a second step the receiver in the ""507 patent determines the energy of the correlation values c(n) that are contained in two windows around this preliminary central window position in accordance with the formula:             E      n        =                                        ∑            K                                j            =                          -              K                                      ⁢                                            "LeftBracketingBar"                              c                ⁡                                  (                                      j                    +                                          m                      w                                        +                    n                                    )                                            "RightBracketingBar"                                      2              ⁢                              xe2x80x83                                              ⁢                      xe2x80x83                    ⁢          n                    =      0        ,  1
where 2K+1=N, that is the number of correlation values in each window, for example, 5. In the example illustrated in FIG. 2 applying this technique will result in w being close to 3, the preliminary window center position will be rounded to 3, and two windows centered around positions 3 and 4 are compared with respect to energy contents. The coefficients c(n) of the window that has the largest energy content is output to the equalizer as a channel estimate. The final synchronization position m can be decided in several ways, e.g., by selecting the center position of the window with the largest energy content.
During the introduction of EDGE, an 8 tap channel has been proposed, in order to be able to handle Typical Urban (TU) as well as Hilly Terrain (HT) channels. With the number of channel taps extended from 5 to 8, to employ the method described in U.S. Pat. No. 5,373,507, it will be necessary to calculate 14 correlation products, in order to continue to provide 7 possible synchronization positions. This in turn, would require a center-of-weight search over 14 squared length correlation products. Although, from a purely computational point of view, it may be possible to extend the technique described in U.S. Pat. No. 5,373,507 to perform a center-of-weight search over 14 squared length correlation products, simulations have indicated that some of the additional squared length correlation products which are required by this technique become disturbed by the bits outside of the training sequence. Thus, it would be desirable to perform synchronization in a manner which avoids these disturbances.
One approach is to use a least square error technique instead of the autocorrelation techniques described in U.S. Pat. No. 5,373,507. In general, the least square error technique involves solving the matrix equation H=(ATA)xe2x88x921*ATL, where A is an observation matrix, H is a channel estimate vector and L is a receiver measurement vector. More details regarding this equation and the least square technique are provided below.
Although this least square technique provides an improved result as compared with the autocorrelation technique described above, it does so at the expense of additional processing resources since the number of computations involved in a straightforward application of the least square technique is significantly greater than that associated with the conventional autocorrelation technique. Moreover, since channel estimation and noise estimation must still be performed independently, the total number of computations associated with synchronization, channel estimation and noise estimation requires an unacceptable percentage of the available processing resources.
Accordingly, it would be desirable to arrive at techniques which provide for accurate synchronization in developing radiocommunication systems that employ higher order modulations, while using an acceptable portion of the available processing resources.
It should be emphasized that the terms xe2x80x9ccomprisesxe2x80x9d and xe2x80x9ccomprisingxe2x80x9d, when used in this specification, are taken to specify the presence of stated features, integers, steps or components; but the use of these terms does not preclude the presence or addition of one or more other features, integers, steps, components or groups thereof.
The present invention includes a method and apparatus for acquiring time synchronization, as well as a channel estimate and a noise estimate for a received signal. First, a burst of data which includes a training sequence is received. Then, groups of received training sequence measurements are created. According to an exemplary embodiment seven groups, each containing 19 measurements are created. For each of these groups, a set of linear equations is set up. Next, methods according to the present invention determine the least square estimate by solving the matrix equation H=(ATA)xe2x88x921*ATL for each of the groups.
According to exemplary embodiments of the present invention, this least square estimate is performed in several steps which reduce the number of calculations to be performed. The term ATA is the same for each group and can be computed once prior to computing the least square estimates. The ATL terms are calculated separately for each group. In the process of calculating the ATL term for each group, the ATL term calculated for the previous group can be reused to reduce the total number of calculations. Once the ATA and ATL terms are calculated, then the least square estimate for each group is determined.
The least square estimate is then used to determine a noise estimate for each group. Again, exemplary embodiments of the present invention provide mechanisms for reuse of certain calculations associated with the determination of the noise estimate that reduces the computational complexity associated therewith. Once the noise estimate is calculated for each group, the method determines which of the groups has the lowest valued noise estimate. That group, according to one exemplary embodiment, is chosen as the synchronization group. As an alternative, the group which has the greatest estimated signal-to-noise ratio can be selected as the synchronization group in this step. The least square estimate of the synchronization group is then identified as the channel estimate.
The above features and advantages of the present invention will be more apparent and additional features and advantages of the present invention will be appreciated from the following detailed description of the invention made with reference to the drawings.